Nonstandart logics

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The course covers the parts of modern logic suitable for use in formal methods of computer science: modal and temporal logics as means of analyzing program correctness, intuitionism and type theory as means of formal theorem-proving. In addition, algebraic view on logic is presented, including Boole, modal, temporal and dynamic algebras and basics ot type theory.

Requirements:

To be specified in seminars by tutors.

Syllabus of lectures:

1. Scope and limitations of classical propositional and predicate logic.

2. Modal Propositional Logic.

3. Possible worlds semantics.

4. Correspondence Theorem, modal definability.

5. Systems of modal logics.

6. Extensions of modal logics: CS applications.

7. Temporal operators.

8. Semantics of temporal logics.

9. Logic as algebra: Boole, modal and temporal algebras.

10. Dynamic algebra - programming language semantics.

11. Other extensions of clasical logics: intuitionism.

12. Higher order logics.

13. Basic ideas of type theory.

14. Spare time.

Syllabus of tutorials:

1. Scope and limitations of classical propositional and predicate logic.

2. Modal Propositional Logic.

3. Possible worlds semantics.

4. Correspondence Theorem, modal definability.

5. Systems of modal logics.

6. Extensions of modal logics: CS applications.

7. Temporal operators.

8. Semantics of temporal logics.

9. Logic as algebra: Boole, modal and temporal algebras.

10. Dynamic algebra - programming language semantics.

11. Other extensions of clasical logics: intuitionism.

12. Higher order logics.

13. Basic ideas of type theory.

14. Spare time.

Study Objective:

Study materials:

1. Colin Stirling: Modal and Temporal Preperties of Processes. Springer, 2001

2. Dirk van Dalen: Logic and Structure. Springer, 1980.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Computer Technology - Software Engineering- structured studies (compulsory elective course)
• Computer Technology - System Programming- structured studies (compulsory elective course)
• Computer Technology - Computer Graphics- structured studies (compulsory elective course)
• Computer Technology - Computer Network and Internet- structured studies (compulsory elective course)
• Computer Technology - Designing Digital Systems- structured studies (compulsory elective course)